Model Object appears to be gradually offset from path constraint
The issue is caused by the fact that your origin is not correctly positioned. The animation you applied to your character causes it to move away from its origin, which is why its not working:



To fix this, make your characters walking animation stationary. I would also recommend using the Follow Path Constraint, instead of parenting since it offers more control.

To fix your issue I deleted the movement track in the NLA, and added a key for the correct position to the circle bone.